Study of scalar meson a_0(1450) from B \to a_0(1450)K^* Decays

In the two-quark model supposition for the meson $a_0(1450)$, which can be viewed as either the first excited state (scenario I) or the lowest lying state (scenario II), the branching ratios and the direct CP-violating asymmetries for decays $B^-\to a^{0}_0(1450)K^{*-}, a^{-}_0(1450)K^{*0}$ and $\bar B^0\to a^{+}_0(1450)K^{*-}, a^{0}_0(1450)\bar K^{*0}$ are studied by employing the perturbative QCD factorization approach. We find the following results: (a) For the decays $B^-\to a^{-}_0(1450)K^{*0}, \bar B^0\to a^{+}_0(1450)K^{*-}, a^{0}_0(1450)\bar K^{*0}$, their branching ratios in scenario II are larger than those in scenario I about one order. So it is easy for the experiments to differentiate between the scenario I and II for the meson $a_0(1450)$. (b)For the decay $B^-\to a^{0}_0(1450)K^{*-}$, due to not receiving the enhancement from the $K^*-$emission factorizable diagrams, its penguin operator contributions are the smallest in scenario II, which makes its branching ratio drop into the order of $10^{-6}$. Even so, its branching ratio in scenario II is still larger than that in scenario I about 2.5 times. (c) Even though our predictions are much larger than those from the QCD factorization results, they are still consistent with each other within the large theoretical errors from the annihilation diagrams. (d) We predict the direct CP- violating asymmetry of the decay $B^-\to a^{-}_0(1450)K^{*0}$ is small and only a few percent.Comment: 15 Pages, 5 Figure

Perturbative QCD for B_s \to a_1(1260)(b_1(1235))P(V) Decays

Within the framework of perturbative QCD approach, we study the charmless two-body decays $B_s \to a_1(1260)(b_1(1235))P(V)$ ($P, V$ represent the light pseudo-scalar and vector mesons, respectively.). Using the decays constants and the light-cone distribution amplitudes for these mesons derived from the QCD sum rule method, we find the following results: (a) The decays $\bar B^0_s\to a^{-}_1K^{+}(K^{*+})$ have the contributions from the factorization emission diagrams with a large Wilson coefficient $C_2+C_1/3$ (order of 1), so they have the largest branching ratios and arrive at $10^{-5}$ order. While for the decays $\bar B^0_s\to a^{0}_1 K^{0}(K^{*0})$, the Wilson coefficient is $C_1+C_2/3$ in tree level and color suppressed, so their branching ratios are small and fall in the order of $10^{-7}\sim10^{-8}$. For the decays $\bar B^0_s\to b_1K(K^*)$, all of their branching ratios are of order few times $10^{-6}$. (b) For the pure annihilation type decays $\bar B^0_s\to a_1(b_1)\rho$ except the decays $\bar B^0_s\to a_1\pi$ having large branching ratios of order few times $10^{-6}$, the most other decays have the branching ratios of $10^{-7}$ order. The branching ratios of the decays $\bar B^0_s\to a^0_1(b^0_1)\omega$ are the smallest and fall in the order of $10^{-8}\sim10^{-9}$. (c)The branching ratios and the direct CP-asymmetries of decays $\bar B^0_s\to a^0_1(b_1^0)\eta^{(\prime)}$ are very sensitive to take different Gegenbauer moments for $\eta^{(\prime)}$. (d) Except for the decays $\bar B^0_s\to a^{0}_1 K^{*0}, a^{0}_1\omega, b^{0}_1\omega$, the longitudinal polarization fractions of other $\bar B^0_s\to a_1(b_1)V$ decays are very large and more than 90%. (e) Compared with decays $\bar B^0_s\to a_1(b_1)P$, most of $\bar B^0_s\to a_1(b_1)V$ decays have smaller direct CP asymmetries.Comment: 17 pages, 5 figure

Study of scalar meson f_0(980) and K_0^*(1430) from B \to f_0(980)\rho(\omega, \phi) and B \to K^*_0(1430)\rho(\omega) Decays

In the two-quark model supposition for $f_0(980)$ and $K_0^{*}(1430)$, the branching ratios and the direct CP-violating asymmetries for decays $\bar{B}^0\to f_0(980)\rho^0(\omega,\phi), K^{*0}_0(1430)\rho^0(\omega), K^{*-}_0(1430)\rho^+$ and $B^-\to f_0(980)\rho^-, K^{*0}_0(1430)\rho^-, K^{*-}_0(1430)\rho^0(\omega)$ are studied by employing the perturbative QCD (PQCD)factorization approach. we find the following results: (a) if the scalar meson $f_0(980)$ is viewed as a mixture of $s\bar s$ and $(u\bar u+d\bar d)/\sqrt{2}$, the branching ratios of the decays $\bar{B}^0\to f_0(980)\rho^0(\omega,\phi)$ and $B^-\to f_0(980)\rho^-$, which are induced by $b\to d$ transition, are smaller than the currently experimental upper limits, and the predictions for the decay $\bar{B}^0\to f_0(980)\omega, B^-\to f_0(980)\rho^-$ are not far away from their limits; (b) in the decays $B\to K^*_0(1430)\rho(\omega)$, which are induced by $b\to s$ transition, the branch ratio of $\bar B^0\to K^{*0}_0(1430)\rho^0$ is the smallest one in two scenarios, at the order of $10^{-7}$ for scenario I, about $4.8\times10^{-6}$ for scenario II; (c) the direct CP-asymmetries of the decays $B\to f_0(980)\rho(\omega)$ have a strong dependent on the mixing angle $\theta$: they are large in the range of $25^\circ<\theta<40^\circ$, and small in the range of $140^\circ<\theta<165^\circ$, while the direct CP-asymmetries of the decays $B\to K^{*}_0(1430)\rho(\omega)$ are not large in both scenarios and most of them are less than 20% in size.Comment: 17 pages, 5 figures, minor corrections, typos removed, accepted for publication in Phys. Rev.

The decays B→Ψ(2S)π(K),ηc(2S)π(K)B\to \Psi(2S)\pi(K),\eta_c(2S)\pi(K) in the pQCD approach beyond the leading-order

Two body $B$ meson decays involving the radially excited meson $\psi(2S)/\eta_c(2S)$ in the final states are studied by using the perturbative QCD (pQCD) approach. We find that: (a) The branching ratios for the decays involving $K$ meson are predicted as $Br(B^+\to\psi(2S)K^+)=(5.37^{+1.85}_{-2.22})\times10^{-4}, Br(B^0\to\psi(2S)K^0)=(4.98^{+1.71}_{-2.06})\times10^{-4}, Br(B^+\to\eta_c(2S)K^+)=(3.54^{+3.18}_{-3.09})\times10^{-4}$, which are consistent well with the present data when including the next-to-leading-order (NLO) effects. Here the NLO effects are from the vertex corrections and the NLO Wilson coefficients. The large errors in the decay $B^+\to\eta_c(2S)K^+$ are mainly induced by using the decay constant $f_{\eta_c(2S)}=0.243^{+0.079}_{-0.111}$ GeV with large uncertainties. (b) While there seems to be some room left for other higher order corrections or the non-perturbative long distance contributions in the decays involving $\pi$ meson, $Br(B^+\to\psi(2S)\pi^+)=(1.17^{+0.42}_{-0.50})\times10^{-5}, Br(B^0\to\psi(2S)\pi^0)=0.54^{+0.20}_{-0.23}\times10^{-5}$, which are smaller than the present data. The results for other decays can be tested at the running LHCb and forthcoming Super-B experiments. (c) There is no obvious evidence of the direct CP violation being seen in the decays $B\to \psi(2S)\pi(K), \eta_c(2S)\pi(K)$ in the present experiments, which is supported by our calculations. If a few percent value is confirmed in the future , it would indicate new physics definitely.Comment: 11 pages, 3 figures. arXiv admin note: text overlap with arXiv:1705.0052

Three body radiative decay Bs→ϕKˉ0γB_s\to \phi \bar K^0 \gamma in the PQCD approach

We study the three body radiative decay $B_s\to \phi \bar K^0 \gamma$ by introducing the $\phi K$ pair distribution amplitudes (DAs) in the perturbative QCD approach. This nonperturbative inputs, the two meson DAs, is very important to simplify the calculations. Besides the dominant electromagnetic penguin operator $O_{7\gamma}$, the subleading contributions from chromomagnetic penguin operator $O_{8g}$, quark-loop corrections and annihilation type amplitudes are also considered. We find that the branching ratio for the decay $B_s\to \phi \bar K^0 \gamma$ is about $(9.26^{+1.79+3.12+0.64}_{-1.61-3.86-0.49})\times10^{-8}$, which is much smaller compared with that for the decay $B^0\to \phi K^0\gamma$. It is mainly because that the former decay induces by $b\to d\gamma$ with small CKM matrix element being proportional to $\lambda^3$. The prediction for the direct CP asymmetry is $A^{dir}_{CP}(B_s\to \phi \bar K^0 \gamma)=(-4.1^{+0.4+1.7+0.2}_{-0.6-1.2-0.1})\%$, which is well consistent with the result from the U-spin symmetry approach. we also predict the $B_s \to\phi \bar K^0\gamma$ decay spectrum, which exhibits a maximu at the $\phi K$ invariant masss around 1.95 GeV.Comment: 17 pages,6 figures, Accepted for publication in EPJ

B\to K_1\pi(K) decays in the perturbative QCD approach

Within the framework of the perturbative QCD approach, we study the two-body charmless decays $B\to K_1(1270)(K_1(1400))\pi(K)$. We find the following results: (i) The decays $\bar B^0\to K_1(1270)^+\pi^-, K_1(1400)^+\pi^-$ are incompatible with the present experimental data. There exists a similar situation for the decays $\bar B^0\to a_1(1260)^+K^-, b_1(1235)^+K^-$, which are usually considered that the nonperturbative contributions are needed to explain the data. But the difference is that the nonperturbative contributions seem to play opposite roles in these two groups of decays.(ii) The pure annihilation type decays $\bar B^0\to K_1^{\pm}(1270)K^{\mp}, K_1^{\pm}(1400)K^{\mp}$ are good channels to test whether an approach can be used to calculate correctly the strength of the penguin-annihilation amplitudes. Their branching ratios are predicted at $10^{-7}$ order, which are larger than the QCDF results. (iii) The dependence of the direct CP-violating asymmetries of these decays on the mixing angle $\theta_{K_1}$ are also considered.Comment: 18 pages, 4 figure